PRP Records

Probable Primes Top 10000

(295148 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
9751(44*10^98284-719)/998285Robert Price12/2017
9752(5985^26021-1)/598498280Serge Batalov06/2022
975323466^15419+15419^2346698277Hans Havermann02/2020
97542^326421-279757398263Enzo Doria04/2016
97552^326401+1609598257Lelio R Paula07/2016
9756(6494^25771-1)/649398249Serge Batalov06/2022
97577^116240-116240^798235Norbert Schneider05/2017
975817^79826-7898222Lelio R Paula08/2016
97592^326268-80998217Yves Minet04/2011
976022659^21590+21590^2265998210Hans Havermann10/2019
976122268^22587-22587^2226898202Norbert Schneider08/2020
9762(418*10^98199+23)/998201Robert Price08/2017
976312*10^98198-798200Robert Price11/2017
976415^83496-7698199Lelio R Paula08/2016
9765(10223*2^326179+1)/612598190Lelio R Paula07/2014
97669*5^140471-498186Lelio R Paula11/2014
9767(35103^21601-1)/3510298180Serge Batalov06/2022
976922774^20455+20455^2277498175Hans Havermann07/2020
9768(4516^26863-1)/451598175Serge Batalov06/2022
97702^326069-238398157Yves Minet10/2013
9771(9661^24631-1)/966098152Serge Batalov06/2022
9772(4175^27109-1)/417498149Serge Batalov06/2022
9773(57801^20611-1)/5780098144Serge Batalov06/2022
97742^325973+118598128Lelio R Paula07/2016
9775(25*2^325949-1)/1798121Lelio R Paula02/2014
97762^325945-184726998120Enzo Doria07/2015
97778*10^98111-6798112Robert Price10/2017
9778(2^325902+1138)/298106Stefano Morozzi09/2020
9779(215^42061-1)/21498103Serge Batalov06/2022
9780(6775^25609-1)/677498102Serge Batalov06/2022
9781(6718^25633-1)/671798100Serge Batalov06/2022
97822^325866+1598096Lelio R Paula12/2012
978322591^21952+21952^2259198079Hans Havermann02/2020
97842^325765+197430598066Enzo Doria06/2016
97852^325733-5869598056Lelio R Paula07/2016
9786(7*10^98055-529)/998055Robert Price08/2021
97872^325717-364598051Lelio R Paula07/2016
9788(2^325704+718)/298047Stefano Morozzi09/2020
9789(15679^23371-1)/1567898045Serge Batalov06/2022
9790(23342^22441-1)/2334198022Serge Batalov06/2022
979123968^12293+12293^2396898021Hans Havermann11/2019
9793(23*2^325583-1)/2198011Lelio R Paula02/2014
9792(128678^19321-1)/(128678^139-1)98011Ryan Propper11/2023
9794(7*10^98007-13)/398008Robert Price06/2016
9795(2^325544+1110)/297999Stefano Morozzi09/2020
97962^325512-45995997989Enzo Doria05/2015
9797(2^325492+682)/297983Stefano Morozzi09/2020
9798(3^205354-8)/1797978Lelio R Paula09/2013
97992^325433+7681797966Enzo Doria05/2016
98005*10^97963+8197964Robert Price08/2017
9801(9996^24649-1)/(9996^157-1)97964Ryan Propper11/2023
9802(13208^23773-1)/1320797961Serge Batalov06/2022
98032^325390-10906197953Enzo Doria04/2014
9804(55*10^97940+323)/997941Robert Price10/2021
980513^87921+2497940Lelio R Paula08/2016
980610^97930+18827797931Patrick De Geest09/2022
980810^97930-700000197930Robert Price06/2021
980710^97930-6695197930Patrick De Geest09/2022
9809961^32831-960^3283197926Jean-Louis Charton02/2011
9810(17968^23017-1)/1796797922Serge Batalov06/2022
9811(3337^27793-1)/333697922Serge Batalov06/2022
981322600^21499+21499^2260097913Hans Havermann05/2020
9812(18703^22921-1)/1870297913Serge Batalov06/2022
98142^325215+1290997900Lelio R Paula07/2016
981522619^21286+21286^2261997898Hans Havermann04/2020
9816(126852^19321-1)/(126852^139-1)97892Ryan Propper11/2023
9817(85*10^97876-49)/997877Robert Price12/2020
98187*10^97874-6997875Robert Price01/2017
98195*10^97869-6397870Robert Price04/2021
9820(643*32^65022-23)/3197870Eric Chen04/2023
9822(17^79537+5^79537)/2297865Robert Price06/2013
982115^83212+2297865Lelio R Paula08/2016
98232^325087-10905797861Enzo Doria04/2014
98242^325074+187065797858Enzo Doria05/2016
98262^325066-211197855Yves Minet08/2013
9825CopelandErdos(97855)97855Eric W. Weisstein10/2015
9827(8694^24841-1)/869397851Serge Batalov06/2022
9828(21159^22621-1)/2115897843Serge Batalov06/2022
982926660^4677+4677^2666097842Hans Havermann12/2019
983018^77944-8997841Lelio R Paula07/2016
9831119^47136+11897833Norbert Schneider09/2018
98326^125720-1766397830Enzo Doria02/2013
9833(73640^20101-1)/7363997829Serge Batalov06/2022
98342^324972-206997827Yves Minet05/2013
98352^324958-469197823Yves Minet05/2019
9836(8087^25033-1)/808697820Serge Batalov06/2022
98372^324944-278831997818Enzo Doria03/2016
983922845^19112+19112^2284597807Hans Havermann10/2019
9838(317^39107-1)/31697807Anonymous04/2024
9840(2^324898+1270)/297804Stefano Morozzi09/2020
98424*10^97799-997800Erik Branger11/2013
98412^324882+57729457597800Lelio R Paula09/2016
98432^324863-186792197794Enzo Doria04/2016
98446^125662-1847397785Enzo Doria03/2013
984512^90604+1197779Lelio R Paula07/2016
9846(29*10^97751+49)/397752Robert Price09/2021
9847(37108^21391-1)/3710797741Serge Batalov06/2022
98485^139830+2497737Lelio R Paula04/2016
9849(2^324672+1198)/297736Stefano Morozzi09/2020
9850(101*10^97724+7)/997726Robert Price02/2022
98512^324612+115597718Lelio R Paula07/2016
9852(2^324597+3542)/297714Stefano Morozzi09/2020
985319^76404-4497702Lelio R Paula07/2016
9854(5939^25889-1)/593897694Serge Batalov06/2022
98562^324505-298397686Yves Minet04/2011
9855(7740^25121-1)/773997686Serge Batalov06/2022
9857(144^45259+1)/14597684Paul Bourdelais08/2019
9858(31*2^324496-1)/4597683Lelio R Paula02/2014
9859(11234^24109-1)/1123397651Serge Batalov06/2022
98606^125488-1784397649Enzo Doria02/2013
9861(2^324350+3198)/297639Stefano Morozzi09/2020
9862(75638^20011-1)/7563797624Serge Batalov06/2022
98637^115515-297622Lelio R Paula09/2013
9864(15672^23269-1)/1567197613Serge Batalov06/2022
9865(89^50069-1)/8897603Paul Bourdelais08/2017
98666^125418-597595Lelio R Paula11/2014
9867(2^324193+3522)/297592Stefano Morozzi09/2020
9868(2422^28837-1)/242197587Serge Batalov06/2022
9869(2^324172+666)/297586Stefano Morozzi09/2020
98702^324091+11154643597562Paul Bourdelais10/2021
98712^324076+115597557Lelio R Paula07/2016
9872(2^324074+9)/1397555Lelio R Paula10/2013
9873(11*10^97539-71)/397540Robert Price04/2022
9874(55459*2^323993+1)/2197536Lelio R Paula07/2014
987513^87557-12^8755797534Jean-Louis Charton12/2008
98762^323946+7393997518Enzo Doria04/2016
98772^323937+186694797515Enzo Doria03/2016
9878(98339^19531-1)/9833897508Serge Batalov06/2022
98806^125290-1853397495Enzo Doria03/2013
9879(2^323870+1650)/297495Stefano Morozzi09/2020
98812^323845+10197488Lelio R Paula12/2012
988218^77662+6597487Lelio R Paula07/2016
988322634^20265+20265^2263497479Hans Havermann04/2020
9884(5533^26041-1)/553297467Serge Batalov06/2022
98852^323772+7677197466Enzo Doria05/2016
98862^323765-11221397463Enzo Doria06/2014
988722730^19389+19389^2273097457Hans Havermann02/2020
98882^323720-655597450Lelio R Paula07/2016
98892^323694-186040197442Enzo Doria03/2016
989020^74886+397429Lelio R Paula06/2016
989124476^9561+9561^2447697427Hans Havermann01/2020
9892(2^323623+1766)/297420Stefano Morozzi09/2020
9893(3250^27739-1)/324997413Serge Batalov06/2022
98953*10^97399+7397400Robert Price04/2016
98947^115252-5097400Lelio R Paula07/2016
9896(4715^26513-1)/471497392Serge Batalov06/2022
98972^323521+21331797390Enzo Doria09/2023
9898224737#+39358197389Nicolas PALAU12/2016
9899(119374^19321-1)/(119374^139-1)97386Ryan Propper11/2023
9900(2^323468+3186)/297374Stefano Morozzi09/2020
9901(2^323456+538)/297370Stefano Morozzi09/2020
990223277^15236+15236^2327797365Hans Havermann07/2020
9904(26*10^97353+31)/397354Robert Price07/2016
9903(2^323403+3510)/297354Stefano Morozzi09/2020
990523756^12519+12519^2375697342Hans Havermann07/2020
990610^97335+27164197336Patrick De Geest09/2022
990810^97335-400000197335Robert Price07/2021
990710^97335-9819397335Patrick De Geest09/2022
9909(637*10^97331+11)/997333Robert Price10/2021
991023991^11402+11402^2399197332Hans Havermann07/2020
991161^54517-60^5451797331Jean-Louis Charton09/2005
9912(38*10^97329+187)/997330Robert Price11/2017
9913(31147^21661-1)/3114697328Serge Batalov06/2022
991486455!4+897319Robert Price09/2019
991522591^20310+20310^2259197316Hans Havermann06/2020
99162^323261-43117397312Harrison Mesh06/2022
9917(3996^27017-1)/399597302Serge Batalov06/2022
991825101^7520+7520^2510197297Hans Havermann05/2020
9919(233*10^97294+7)/397296Robert Price03/2022
9920p(19982)#/2-102497293Robert Price09/2017
9921(65*10^97288+277)/997289Robert Price08/2021
99226^125021-8597286Lelio R Paula08/2016
99232^323164-4735597283Lelio R Paula07/2016
9924(3^203902+4)/3605101515797276Lelio R Paula09/2013
99252^323054-655597249Lelio R Paula07/2016
992622822^18247+18247^2282297249Hans Havermann02/2020
99279*10^97247-2997248Robert Price05/2017
992824382^9735+9735^2438297244Hans Havermann02/2020
9929(31*10^97242+41)/997243Robert Price04/2015
9930GoldenRatioPrime[97241]97241Eric W. Weisstein06/2009
993112^90098-4197233Lelio R Paula07/2016
99322^322928-21692997212Enzo Doria05/2014
9933(16731^23017-1)/1673097209Serge Batalov06/2022
99343*10^97205-6197206Robert Price04/2021
9935(7*2^322896-1)/5797201Lelio R Paula02/2014
9936(35*10^97194-341)/997195Robert Price08/2021
9937(4872^26357-1)/487197194Serge Batalov06/2022
9938(2^322897+5)/314610748997193Lelio R Paula10/2013
9939(796*10^97183-31)/997185Robert Price07/2022
9940(2^322789+2214)/297169Stefano Morozzi09/2020
99412^322725+7576197150Enzo Doria04/2016
9942(13*2^322686+1)/11997138Lelio R Paula11/2013
9943(2175^29101-1)/217497121Serge Batalov06/2022
994422402^21639+21639^2240297118Hans Havermann07/2020
994523399^14128+14128^2339997108Hans Havermann06/2020
9946(2892^28057-1)/289197108Serge Batalov06/2022
9947(9578^24391-1)/957797104Serge Batalov06/2022
9948(2^322525+2606)/297090Stefano Morozzi09/2020
9949(9563^24391-1)/956297087Serge Batalov06/2022
9950(41*10^97085+373)/997086Robert Price04/2017
9951(2^322473+854)/297074Stefano Morozzi02/2021
99522^322413+7797056Lelio R Paula12/2012
99532^322406+17797054Lelio R Paula12/2012
9954(349^38167-1)/34897050Serge Batalov06/2022
9955(14*10^97044+31)/997045Robert Price02/2015
99562^322302+25525597023Lelio R Paula07/2016
99572^322286+21265997018Enzo Doria09/2023
9958(1302^31147-1)/130197008Serge Batalov06/2022
99592^322196-11309396991Enzo Doria07/2014
9960(2^322169+2690)/296983Stefano Morozzi09/2020
9961(49*10^96980+221)/996981Robert Price02/2022
99629*10^96968-4796969Robert Price11/2021
9963(5895^25717-1)/589496962Serge Batalov06/2022
9964(27473^21841-1)/2747296946Serge Batalov06/2022
996523109^15668+15668^2310996943Hans Havermann07/2020
99662^322000-186146996932Enzo Doria03/2016
99672^321971-11274796923Enzo Doria06/2014
996823754^12023+12023^2375496917Hans Havermann07/2020
996911^93062-9296915Lelio R Paula06/2016
9970(37871^21169-1)/3787096914Serge Batalov06/2022
9971(2^321922+2214)/296908Stefano Morozzi09/2020
9972(2^321900+2086)/296902Stefano Morozzi09/2020
9973(11*2^321841-7)/1596884Renaud Lifchitz03/2011
99743^203051+3496880Lelio R Paula05/2016
99752*10^96867-5196868Robert Price11/2017
9976(2^321779+2618)/296865Stefano Morozzi09/2020
9977(64*10^96863-1)/2796864Serge Batalov05/2010
99782^321716-278693996847Enzo Doria03/2016
997922496^20181+20181^2249696844Hans Havermann03/2020
99802^321701-11305396842Enzo Doria07/2014
99812^321700-2863596842Lelio R Paula06/2016
9982(5*2^321691-1)/2796838Lelio R Paula02/2014
99836*10^96835+1396836Robert Price10/2021
99846^124433-12443396828Robert Price01/2014
99852^321631+6996821Lelio R Paula12/2012
9986(27109^21841-1)/2710896820Serge Batalov06/2022
9987(13*2^321606+1)/11996813Lelio R Paula11/2013
9988(5052^26141-1)/505196809Serge Batalov06/2022
9989(46*10^96798-1)/996799Serge Batalov10/2014
9990(59*10^96798+31)/996799Robert Price09/2015
9991(2^321536+2062)/296792Stefano Morozzi09/2020
9992223319#+23122396790Makoto Morimoto02/2016
99932^321519-2863596787Lelio R Paula06/2016
99942^321487-186723796778Enzo Doria03/2016
99952^321461-6396770Lelio R Paula12/2012
9996(16053^23011-1)/1605296770Serge Batalov06/2022
99972^321439+12396763Lelio R Paula12/2012
99982^321434+70996762Lelio R Paula02/2013
99992^321419+2270396757Enzo Doria09/2023
10000(2^321415+554)/296756Stefano Morozzi09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 20 2024 09:22 (Time in France)

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